Contents/Summary

Summary

Multiphysics systems governed by coupled partial differential equations (PDEs) are naturally suited for modular (partitioned) numerical solution strategies. Although widely used in deterministic simulations, several challenges arise in extending the benefits of modularization to stochastic simulation i.e. uncertainty propagation. Monolithic (black-box) Monte Carlo (MC) based sampling methods ignore the potentially exploitable structures within the multiphysics model, and are generally unreliable because the cost of each PDE solve is significantly high. On the other hand, spectral methods, for instance, generalized polynomial chaos (gPC) based methods, would succumb to the curse of dimensionality, if implemented in their standard (traditional) form, as the coupled nature of the model dictates that each module should handle the combined parameter space for uncertainty propagation. In this thesis, we present a practical module-based framework and efficient spectral methods for uncertainty propagation in multiphysics systems with uncertain parameters. Our proposed framework facilitates complete module-based modeling independence, wherein each module only handles its local uncertain parameters, employing the best suited method. Moreover, the proposed reduced non-intrusive (NISP) and reduced intrusive spectral projection (ISP) methods mitigate the curse of dimensionality by constructing reduced dimensional (and order) approximations of the data communicated between modules and iterations. We demonstrate implementations of our proposed methods on several benchmark test problems, and illustrate their superior performance over standard monolithic methods.

Bibliographic information

Publication date

2015

Note

Submitted to the Institute of Computational and Mathematical Engineering.